{"id":98136,"date":"2018-03-11T10:18:48","date_gmt":"2018-03-11T10:18:48","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/polinomios-ortogonalmente-aditivos-y-aplicaciones-orthogonally-additive-polynomials-and-applications\/"},"modified":"2018-03-11T10:18:48","modified_gmt":"2018-03-11T10:18:48","slug":"polinomios-ortogonalmente-aditivos-y-aplicaciones-orthogonally-additive-polynomials-and-applications","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/polinomios-ortogonalmente-aditivos-y-aplicaciones-orthogonally-additive-polynomials-and-applications\/","title":{"rendered":"Polinomios ortogonalmente aditivos y aplicaciones (orthogonally additive polynomials and applications)"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Pablo Linares Briones <\/strong><\/h2>\n<p>En toda teor\u00eda de operadores, tanto lineales como no lineales, es fundamental disponer de teoremas de representaci\u00f3n que nos permitan el manejo de los mismos. Un buen ejemplo de este hecho lo encontramos en el marco del an\u00e1lisis funcional lineal con el teorema de riesz para la representaci\u00f3n integral de los funcionales lineales y continuos sobre un espacio c(k).  en los \u00faltimos a\u00f1os han sido muchos los matem\u00e1ticos interesados en el estudio de operadores no lineales entre espacios de banach, en p articular de polinomios. De nuevo, siempre es deseable disponer de teoremas de representaci\u00f3n que nos permitan estudiar su comportamiento y propiedades. Recientemente, benyamini, lassalle y llavona obtienen un teorema de representaci\u00f3n para la clase de polinomios ortogonalmente aditivos sobre ret\u00edculos de banach. La potencia de este teorema radica en que todo  polinomio n-homog\u00e9neo de esta clase se representa a trav\u00e9s de un funcional lineal  y continuo sobre la n-concavificaci\u00f3n del espacio, es decir, su estudio se reduce a un problema lineal. Este es el punto de partida de esta tesis doctoral.  siguiendo el enfoque mencionado, hemos obtenido numerosas aplicaciones a campos tan diversos como la teor\u00eda espectral de operadores en espacios de hilbert y resultados de estructura de ret\u00edculos de hilbert.  extendemos asimismo la noci\u00f3n de ortogonalidad aditiva al marco de los espacios de riesz, logrando probar el teorema de representaci\u00f3n de polinomios ortogonalmente aditivos en este contexto .  se ha extendido la teor\u00eda cl\u00e1sica de momentos de hausdorff, tanto en el caso real del intervalo [0,1] como en el caso trigonom\u00e9trico del c\u00edrculo unidad t, estudiando el problema multilineal. En este contexto, en el caso [0,1] aparecen tres problem as que denominamos, problema fuerte, problema d\u00e9bil y problema cl\u00e1sico que estudiamos y resolvemos en su totalidad.  finalmente, se  han dado los primeros pasos para el desarrollo de una teor\u00eda similar a la de polinomios ortogonales pero aplicada a u na clase m\u00e1s amplia de funciones poniendo especial atenci\u00f3n en espacios c[0,1] y lp.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Polinomios ortogonalmente aditivos y aplicaciones (orthogonally additive polynomials and applications)<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Polinomios ortogonalmente aditivos y aplicaciones (orthogonally additive polynomials and applications) <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Pablo Linares Briones <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Complutense de Madrid<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 17\/12\/2009<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>Alberto Ibort Latre<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: fernando Bombal gordon <\/li>\n<li>raymond Ryan (vocal)<\/li>\n<li>Antonio  Jos\u00e9 Dur\u00e1n guarde\u00f1o (vocal)<\/li>\n<li>Francisco Marcellan espa\u00f1ol (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Pablo Linares Briones En toda teor\u00eda de operadores, tanto lineales como no lineales, es fundamental disponer de [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"footnotes":""},"categories":[1],"tags":[6173,200814,4782,4781,200813,174092],"class_list":["post-98136","post","type-post","status-publish","format-standard","hentry","category-sin-categoria","tag-alberto-ibort-latre","tag-antonio-jose-duran-guardeno","tag-fernando-bombal-gordon","tag-francisco-marcellan-espanol","tag-pablo-linares-briones","tag-raymond-ryan"],"_links":{"self":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/98136","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/comments?post=98136"}],"version-history":[{"count":0,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/98136\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/media?parent=98136"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/categories?post=98136"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/tags?post=98136"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}